A concept of variety for regular biordered sets.
A multiplication of -varieties of orthodox semigroups
We define semantically a partial multiplication on the lattice of all e–varieties of regular semigroups. In the case that the first factor is an e–variety of orthodox semigroups we describe our multiplication syntactically in terms of biinvariant congruences.
A multiplication of e-varieties of regular -solid semigroups by inverse semigroup varieties
A multiplication of e-varieties of regular -solid semigroups by inverse semigroup varieties is described both semantically and syntactically. The associativity of the multiplication is also proved.
A new example of a limit variety.
A note on normal varieties of monounary algebras
A variety is called normal if no laws of the form are valid in it where is a variable and is not a variable. Let denote the lattice of all varieties of monounary algebras and let be a non-trivial non-normal element of . Then is of the form with some . It is shown that the smallest normal variety containing is contained in for every where denotes the operator of forming choice algebras. Moreover, it is proved that the sublattice of consisting of all normal elements of...
A note on permutability in varieties
A reduction theorem for ring varieties whose subvariety lattice is distributive
We prove a theorem (for arbitrary ring varieties and, in a stronger form, for varieties of associative rings) which basically reduces the problem of a description of varieties with distributive subvariety lattice to the case of algebras over a finite prime field.
A sketch of the lattice of commutative nilpotent semigroup varieties.
A ternary variety generated by lattices
Algebras with principal tolerances
All subvarieties of have finite bases of identities.
All varieties of orthogroups.
An associative operator on the lattice of varieties of inverse semigroups.
An example of the limit variety of semigroups.
Antiatomic retract varieties of monounary algebras